Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 6x + 7$ and $ JT = 7x + 1$ Find $CT$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {6x + 7} = {7x + 1}$ Solve for $x$ $ -x = -6$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 6({6}) + 7$ $ JT = 7({6}) + 1$ $ CJ = 36 + 7$ $ JT = 42 + 1$ $ CJ = 43$ $ JT = 43$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {43} + {43}$ $ CT = 86$